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curve #3775

y² + xy = x³ − 23279145635080x + 39375606629317390400

a-invariants: [1, 0, 0, -23279145635080, 39375606629317390400]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 8843926837830
discriminant (Δ): 137596307097815353794095857724229020160000
Faltings height: 6.6305
naive height: 103.9493
primes of bad reduction: 2, 3, 5, 7, 19, 41, 53, 73, 89, 157
regulator: 260.116717932245790797438116421410092257702096821
submitted by: Daniel Błażewicz
submitted at: 2026-10-01 19:46:53 UTC
last updated: 2026-10-01 19:46:53 UTC

Witness: 5 independent points log in to add more points →

(-5414848, 2583825656)
(4584035/4, 30144482395/8)
(7584992, 17293144616)
(16197386, 62536162772)
(398734760/289, 15442226027320/4913)

Commentary

(u,v) = (5985,2336) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 5.

last edited by Daniel Błażewicz at 2026-10-01 19:46:54 UTC · history

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